1,1,11,0,1.228712," ","integrate(cot(b*x+a),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(b x + a\right)\right)}{b}"," ",0,"log(sin(b*x + a))/b","A",0
2,1,18,0,0.415853," ","integrate(cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{b x + a + \frac{1}{\tan\left(b x + a\right)}}{b}"," ",0,"-(b*x + a + 1/tan(b*x + a))/b","A",0
3,1,23,0,0.357110," ","integrate(cot(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)}{2 \, b}"," ",0,"-1/2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b","A",0
4,1,34,0,0.416458," ","integrate(cot(b*x+a)^4,x, algorithm=""maxima"")","\frac{3 \, b x + 3 \, a + \frac{3 \, \tan\left(b x + a\right)^{2} - 1}{\tan\left(b x + a\right)^{3}}}{3 \, b}"," ",0,"1/3*(3*b*x + 3*a + (3*tan(b*x + a)^2 - 1)/tan(b*x + a)^3)/b","A",0
5,1,38,0,0.327104," ","integrate(cot(b*x+a)^5,x, algorithm=""maxima"")","\frac{\frac{4 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4}} + 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)}{4 \, b}"," ",0,"1/4*((4*sin(b*x + a)^2 - 1)/sin(b*x + a)^4 + 2*log(sin(b*x + a)^2))/b","A",0
6,1,44,0,0.625667," ","integrate(cot(b*x+a)^6,x, algorithm=""maxima"")","-\frac{15 \, b x + 15 \, a + \frac{15 \, \tan\left(b x + a\right)^{4} - 5 \, \tan\left(b x + a\right)^{2} + 3}{\tan\left(b x + a\right)^{5}}}{15 \, b}"," ",0,"-1/15*(15*b*x + 15*a + (15*tan(b*x + a)^4 - 5*tan(b*x + a)^2 + 3)/tan(b*x + a)^5)/b","A",0
7,1,48,0,0.397747," ","integrate(cot(b*x+a)^7,x, algorithm=""maxima"")","-\frac{\frac{18 \, \sin\left(b x + a\right)^{4} - 9 \, \sin\left(b x + a\right)^{2} + 2}{\sin\left(b x + a\right)^{6}} + 6 \, \log\left(\sin\left(b x + a\right)^{2}\right)}{12 \, b}"," ",0,"-1/12*((18*sin(b*x + a)^4 - 9*sin(b*x + a)^2 + 2)/sin(b*x + a)^6 + 6*log(sin(b*x + a)^2))/b","A",0
8,1,54,0,0.543120," ","integrate(cot(b*x+a)^8,x, algorithm=""maxima"")","\frac{105 \, b x + 105 \, a + \frac{105 \, \tan\left(b x + a\right)^{6} - 35 \, \tan\left(b x + a\right)^{4} + 21 \, \tan\left(b x + a\right)^{2} - 15}{\tan\left(b x + a\right)^{7}}}{105 \, b}"," ",0,"1/105*(105*b*x + 105*a + (105*tan(b*x + a)^6 - 35*tan(b*x + a)^4 + 21*tan(b*x + a)^2 - 15)/tan(b*x + a)^7)/b","A",0
9,1,197,0,0.421772," ","integrate((c*cot(b*x+a))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(10 \, \sqrt{2} c^{\frac{5}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right) + 10 \, \sqrt{2} c^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right) + 5 \, \sqrt{2} c^{\frac{5}{2}} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right) - 5 \, \sqrt{2} c^{\frac{5}{2}} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right) - 40 \, c^{2} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + 8 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{5}{2}}\right)} c}{20 \, b}"," ",0,"-1/20*(10*sqrt(2)*c^(5/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c)) + 10*sqrt(2)*c^(5/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c)) + 5*sqrt(2)*c^(5/2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a)) - 5*sqrt(2)*c^(5/2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a)) - 40*c^2*sqrt(c/tan(b*x + a)) + 8*(c/tan(b*x + a))^(5/2))*c/b","A",0
10,1,185,0,0.552451," ","integrate((c*cot(b*x+a))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 \, c^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}}\right)} - 8 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{3}{2}}\right)} c}{12 \, b}"," ",0,"1/12*(3*c^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) - sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c) + sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c)) - 8*(c/tan(b*x + a))^(3/2))*c/b","A",0
11,1,179,0,0.497234," ","integrate((c*cot(b*x+a))^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} \sqrt{c} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right) + 2 \, \sqrt{2} \sqrt{c} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right) + \sqrt{2} \sqrt{c} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right) - \sqrt{2} \sqrt{c} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right) - 8 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)} c}{4 \, b}"," ",0,"1/4*(2*sqrt(2)*sqrt(c)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c)) + 2*sqrt(2)*sqrt(c)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c)) + sqrt(2)*sqrt(c)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a)) - sqrt(2)*sqrt(c)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a)) - 8*sqrt(c/tan(b*x + a)))*c/b","A",0
12,1,165,0,0.416482," ","integrate((c*cot(b*x+a))^(1/2),x, algorithm=""maxima"")","-\frac{c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}}\right)}}{4 \, b}"," ",0,"-1/4*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) - sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c) + sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c))/b","A",0
13,1,165,0,0.430568," ","integrate(1/(c*cot(b*x+a))^(1/2),x, algorithm=""maxima"")","-\frac{c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{c^{\frac{3}{2}}}\right)}}{4 \, b}"," ",0,"-1/4*c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/c^(3/2) + sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/c^(3/2) - sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/c^(3/2))/b","A",0
14,1,187,0,0.514390," ","integrate(1/(c*cot(b*x+a))^(3/2),x, algorithm=""maxima"")","\frac{c {\left(\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}}}{c^{2}} + \frac{8}{c^{2} \sqrt{\frac{c}{\tan\left(b x + a\right)}}}\right)}}{4 \, b}"," ",0,"1/4*c*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) - sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c) + sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c))/c^2 + 8/(c^2*sqrt(c/tan(b*x + a))))/b","A",0
15,1,188,0,0.528805," ","integrate(1/(c*cot(b*x+a))^(5/2),x, algorithm=""maxima"")","\frac{c {\left(\frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{c^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{c^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{c^{\frac{3}{2}}}\right)}}{c^{2}} + \frac{8}{c^{2} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{3}{2}}}\right)}}{12 \, b}"," ",0,"1/12*c*(3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/c^(3/2) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/c^(3/2) + sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/c^(3/2) - sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/c^(3/2))/c^2 + 8/(c^2*(c/tan(b*x + a))^(3/2)))/b","A",0
16,1,205,0,0.421121," ","integrate(1/(c*cot(b*x+a))^(7/2),x, algorithm=""maxima"")","-\frac{c {\left(\frac{5 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} + 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{c} - 2 \, \sqrt{\frac{c}{\tan\left(b x + a\right)}}\right)}}{2 \, \sqrt{c}}\right)}{\sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}} + \frac{\sqrt{2} \log\left(-\sqrt{2} \sqrt{c} \sqrt{\frac{c}{\tan\left(b x + a\right)}} + c + \frac{c}{\tan\left(b x + a\right)}\right)}{\sqrt{c}}\right)}}{c^{4}} - \frac{8 \, {\left(c^{2} - \frac{5 \, c^{2}}{\tan\left(b x + a\right)^{2}}\right)}}{c^{4} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{5}{2}}}\right)}}{20 \, b}"," ",0,"-1/20*c*(5*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(c) + 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(c) - 2*sqrt(c/tan(b*x + a)))/sqrt(c))/sqrt(c) - sqrt(2)*log(sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c) + sqrt(2)*log(-sqrt(2)*sqrt(c)*sqrt(c/tan(b*x + a)) + c + c/tan(b*x + a))/sqrt(c))/c^4 - 8*(c^2 - 5*c^2/tan(b*x + a)^2)/(c^4*(c/tan(b*x + a))^(5/2)))/b","A",0
17,1,196,0,0.500937," ","integrate((c*cot(b*x+a))^(4/3),x, algorithm=""maxima"")","\frac{{\left(\sqrt{3} c^{\frac{1}{3}} \log\left(\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right) - \sqrt{3} c^{\frac{1}{3}} \log\left(-\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right) + 2 \, c^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} c^{\frac{1}{3}} + 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right) + 2 \, c^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} c^{\frac{1}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right) + 4 \, c^{\frac{1}{3}} \arctan\left(\frac{\left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right) - 12 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}\right)} c}{4 \, b}"," ",0,"1/4*(sqrt(3)*c^(1/3)*log(sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3)) - sqrt(3)*c^(1/3)*log(-sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3)) + 2*c^(1/3)*arctan((sqrt(3)*c^(1/3) + 2*(c/tan(b*x + a))^(1/3))/c^(1/3)) + 2*c^(1/3)*arctan(-(sqrt(3)*c^(1/3) - 2*(c/tan(b*x + a))^(1/3))/c^(1/3)) + 4*c^(1/3)*arctan((c/tan(b*x + a))^(1/3)/c^(1/3)) - 12*(c/tan(b*x + a))^(1/3))*c/b","A",0
18,1,182,0,0.543059," ","integrate((c*cot(b*x+a))^(2/3),x, algorithm=""maxima"")","\frac{{\left(\frac{\sqrt{3} \log\left(\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{1}{3}}} - \frac{\sqrt{3} \log\left(-\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \arctan\left(\frac{\sqrt{3} c^{\frac{1}{3}} + 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \arctan\left(-\frac{\sqrt{3} c^{\frac{1}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{4 \, \arctan\left(\frac{\left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}\right)} c}{4 \, b}"," ",0,"1/4*(sqrt(3)*log(sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(1/3) - sqrt(3)*log(-sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(1/3) - 2*arctan((sqrt(3)*c^(1/3) + 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(1/3) - 2*arctan(-(sqrt(3)*c^(1/3) - 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(1/3) - 4*arctan((c/tan(b*x + a))^(1/3)/c^(1/3))/c^(1/3))*c/b","A",0
19,1,102,0,0.485244," ","integrate((c*cot(b*x+a))^(1/3),x, algorithm=""maxima"")","-\frac{c {\left(\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(c^{\frac{2}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{2}{3}}} + \frac{\log\left(c^{\frac{4}{3}} - c^{\frac{2}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{4}{3}}\right)}{c^{\frac{2}{3}}} - \frac{2 \, \log\left(c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{2}{3}}}\right)}}{4 \, b}"," ",0,"-1/4*c*(2*sqrt(3)*arctan(-1/3*sqrt(3)*(c^(2/3) - 2*(c/tan(b*x + a))^(2/3))/c^(2/3))/c^(2/3) + log(c^(4/3) - c^(2/3)*(c/tan(b*x + a))^(2/3) + (c/tan(b*x + a))^(4/3))/c^(2/3) - 2*log(c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(2/3))/b","A",0
20,1,103,0,0.418316," ","integrate(1/(c*cot(b*x+a))^(1/3),x, algorithm=""maxima"")","-\frac{c {\left(\frac{2 \, \sqrt{3} \arctan\left(-\frac{\sqrt{3} {\left(c^{\frac{2}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} - \frac{\log\left(c^{\frac{4}{3}} - c^{\frac{2}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{4}{3}}\right)}{c^{\frac{4}{3}}} + \frac{2 \, \log\left(c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{4}{3}}}\right)}}{4 \, b}"," ",0,"-1/4*c*(2*sqrt(3)*arctan(-1/3*sqrt(3)*(c^(2/3) - 2*(c/tan(b*x + a))^(2/3))/c^(2/3))/c^(4/3) - log(c^(4/3) - c^(2/3)*(c/tan(b*x + a))^(2/3) + (c/tan(b*x + a))^(4/3))/c^(4/3) + 2*log(c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(4/3))/b","A",0
21,1,182,0,0.420968," ","integrate(1/(c*cot(b*x+a))^(2/3),x, algorithm=""maxima"")","-\frac{c {\left(\frac{\sqrt{3} \log\left(\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{5}{3}}} - \frac{\sqrt{3} \log\left(-\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \arctan\left(\frac{\sqrt{3} c^{\frac{1}{3}} + 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \arctan\left(-\frac{\sqrt{3} c^{\frac{1}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{4 \, \arctan\left(\frac{\left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}}{4 \, b}"," ",0,"-1/4*c*(sqrt(3)*log(sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(5/3) - sqrt(3)*log(-sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(5/3) + 2*arctan((sqrt(3)*c^(1/3) + 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(5/3) + 2*arctan(-(sqrt(3)*c^(1/3) - 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(5/3) + 4*arctan((c/tan(b*x + a))^(1/3)/c^(1/3))/c^(5/3))/b","A",0
22,1,204,0,0.485917," ","integrate(1/(c*cot(b*x+a))^(4/3),x, algorithm=""maxima"")","-\frac{c {\left(\frac{\frac{\sqrt{3} \log\left(\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{1}{3}}} - \frac{\sqrt{3} \log\left(-\sqrt{3} c^{\frac{1}{3}} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}} + c^{\frac{2}{3}} + \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{2}{3}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \arctan\left(\frac{\sqrt{3} c^{\frac{1}{3}} + 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \arctan\left(-\frac{\sqrt{3} c^{\frac{1}{3}} - 2 \, \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{4 \, \arctan\left(\frac{\left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}}{c^{2}} - \frac{12}{c^{2} \left(\frac{c}{\tan\left(b x + a\right)}\right)^{\frac{1}{3}}}\right)}}{4 \, b}"," ",0,"-1/4*c*((sqrt(3)*log(sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(1/3) - sqrt(3)*log(-sqrt(3)*c^(1/3)*(c/tan(b*x + a))^(1/3) + c^(2/3) + (c/tan(b*x + a))^(2/3))/c^(1/3) - 2*arctan((sqrt(3)*c^(1/3) + 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(1/3) - 2*arctan(-(sqrt(3)*c^(1/3) - 2*(c/tan(b*x + a))^(1/3))/c^(1/3))/c^(1/3) - 4*arctan((c/tan(b*x + a))^(1/3)/c^(1/3))/c^(1/3))/c^2 - 12/(c^2*(c/tan(b*x + a))^(1/3)))/b","A",0
23,0,0,0,0.000000," ","integrate(cot(b*x+a)^n,x, algorithm=""maxima"")","\int \cot\left(b x + a\right)^{n}\,{d x}"," ",0,"integrate(cot(b*x + a)^n, x)","F",0
24,0,0,0,0.000000," ","integrate((b*cot(d*x+c))^n,x, algorithm=""maxima"")","\int \left(b \cot\left(d x + c\right)\right)^{n}\,{d x}"," ",0,"integrate((b*cot(d*x + c))^n, x)","F",0
25,1,30,0,0.494452," ","integrate((a*cot(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a^{\frac{3}{2}} \log\left(\tan\left(x\right)^{2} + 1\right) - a^{\frac{3}{2}} \log\left(\tan\left(x\right)\right) - \frac{a^{\frac{3}{2}}}{2 \, \tan\left(x\right)^{2}}"," ",0,"1/2*a^(3/2)*log(tan(x)^2 + 1) - a^(3/2)*log(tan(x)) - 1/2*a^(3/2)/tan(x)^2","A",0
26,1,20,0,0.453615," ","integrate((a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{a} \log\left(\tan\left(x\right)^{2} + 1\right) + \sqrt{a} \log\left(\tan\left(x\right)\right)"," ",0,"-1/2*sqrt(a)*log(tan(x)^2 + 1) + sqrt(a)*log(tan(x))","A",0
27,1,12,0,0.495314," ","integrate(1/(a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, \sqrt{a}}"," ",0,"1/2*log(tan(x)^2 + 1)/sqrt(a)","A",0
28,1,22,0,0.568201," ","integrate(1/(a*cot(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)^{2}}{2 \, a^{\frac{3}{2}}} - \frac{\log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, a^{\frac{3}{2}}}"," ",0,"1/2*tan(x)^2/a^(3/2) - 1/2*log(tan(x)^2 + 1)/a^(3/2)","A",0
29,1,113,0,0.531168," ","integrate((a*cot(x)^3)^(3/2),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, \sqrt{2} \sqrt{a} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + 2 \, \sqrt{2} \sqrt{a} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + \sqrt{2} \sqrt{a} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) - \sqrt{2} \sqrt{a} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right)\right)} a + \frac{2 \, a^{\frac{3}{2}}}{3 \, \tan\left(x\right)^{\frac{3}{2}}} - \frac{2 \, a^{\frac{3}{2}}}{7 \, \tan\left(x\right)^{\frac{7}{2}}}"," ",0,"1/4*(2*sqrt(2)*sqrt(a)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) + 2*sqrt(2)*sqrt(a)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) + sqrt(2)*sqrt(a)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) - sqrt(2)*sqrt(a)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1))*a + 2/3*a^(3/2)/tan(x)^(3/2) - 2/7*a^(3/2)/tan(x)^(7/2)","A",0
30,1,94,0,0.458238," ","integrate((a*cot(x)^3)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right)\right)} \sqrt{a} - \frac{2 \, \sqrt{a}}{\sqrt{\tan\left(x\right)}}"," ",0,"-1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1))*sqrt(a) - 2*sqrt(a)/sqrt(tan(x))","A",0
31,1,94,0,0.532502," ","integrate(1/(a*cot(x)^3)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) - \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right)}{4 \, \sqrt{a}} + \frac{2 \, \sqrt{\tan\left(x\right)}}{\sqrt{a}}"," ",0,"-1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) + sqrt(2)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) - sqrt(2)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1))/sqrt(a) + 2*sqrt(tan(x))/sqrt(a)","A",0
32,1,109,0,0.459800," ","integrate(1/(a*cot(x)^3)^(3/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(x\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(x\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(x\right)} + \tan\left(x\right) + 1\right)}{4 \, a^{\frac{3}{2}}} + \frac{2 \, {\left(3 \, \sqrt{a} \tan\left(x\right)^{\frac{7}{2}} - 7 \, \sqrt{a} \tan\left(x\right)^{\frac{3}{2}}\right)}}{21 \, a^{2}}"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(x)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(x)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(x)) + tan(x) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(x)) + tan(x) + 1))/a^(3/2) + 2/21*(3*sqrt(a)*tan(x)^(7/2) - 7*sqrt(a)*tan(x)^(3/2))/a^2","A",0
33,1,37,0,0.475252," ","integrate((a*cot(x)^4)^(3/2),x, algorithm=""maxima"")","-a^{\frac{3}{2}} x - \frac{15 \, a^{\frac{3}{2}} \tan\left(x\right)^{4} - 5 \, a^{\frac{3}{2}} \tan\left(x\right)^{2} + 3 \, a^{\frac{3}{2}}}{15 \, \tan\left(x\right)^{5}}"," ",0,"-a^(3/2)*x - 1/15*(15*a^(3/2)*tan(x)^4 - 5*a^(3/2)*tan(x)^2 + 3*a^(3/2))/tan(x)^5","A",0
34,1,16,0,0.478963," ","integrate((a*cot(x)^4)^(1/2),x, algorithm=""maxima"")","-\sqrt{a} x - \frac{\sqrt{a}}{\tan\left(x\right)}"," ",0,"-sqrt(a)*x - sqrt(a)/tan(x)","A",0
35,1,13,0,0.456234," ","integrate(1/(a*cot(x)^4)^(1/2),x, algorithm=""maxima"")","-\frac{x}{\sqrt{a}} + \frac{\tan\left(x\right)}{\sqrt{a}}"," ",0,"-x/sqrt(a) + tan(x)/sqrt(a)","A",0
36,1,29,0,0.453355," ","integrate(1/(a*cot(x)^4)^(3/2),x, algorithm=""maxima"")","\frac{3 \, \tan\left(x\right)^{5} - 5 \, \tan\left(x\right)^{3} + 15 \, \tan\left(x\right)}{15 \, a^{\frac{3}{2}}} - \frac{x}{a^{\frac{3}{2}}}"," ",0,"1/15*(3*tan(x)^5 - 5*tan(x)^3 + 15*tan(x))/a^(3/2) - x/a^(3/2)","A",0
37,0,0,0,0.000000," ","integrate((b*cot(d*x+c)^p)^n,x, algorithm=""maxima"")","\int \left(b \cot\left(d x + c\right)^{p}\right)^{n}\,{d x}"," ",0,"integrate((b*cot(d*x + c)^p)^n, x)","F",0
38,0,0,0,0.000000," ","integrate((a*(b*cot(d*x+c))^p)^n,x, algorithm=""maxima"")","\int \left(\left(b \cot\left(d x + c\right)\right)^{p} a\right)^{n}\,{d x}"," ",0,"integrate(((b*cot(d*x + c))^p*a)^n, x)","F",0
39,0,0,0,0.000000," ","integrate((b*cot(f*x+e))^n*(a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \left(b \cot\left(f x + e\right)\right)^{n} \left(a \sin\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*cot(f*x + e))^n*(a*sin(f*x + e))^m, x)","F",0
40,0,0,0,0.000000," ","integrate((a*cos(f*x+e))^m*(b*cot(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \cos\left(f x + e\right)\right)^{m} \left(b \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*cos(f*x + e))^m*(b*cot(f*x + e))^n, x)","F",0
41,0,0,0,0.000000," ","integrate((a*cot(f*x+e))^m*(b*cot(f*x+e))^n,x, algorithm=""maxima"")","\int \left(a \cot\left(f x + e\right)\right)^{m} \left(b \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*cot(f*x + e))^m*(b*cot(f*x + e))^n, x)","F",0
42,0,0,0,0.000000," ","integrate((b*cot(f*x+e))^n*(a*sec(f*x+e))^m,x, algorithm=""maxima"")","\int \left(b \cot\left(f x + e\right)\right)^{n} \left(a \sec\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*cot(f*x + e))^n*(a*sec(f*x + e))^m, x)","F",0
43,1,84,0,0.346042," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^6,x, algorithm=""maxima"")","-\frac{\frac{\left(\frac{d}{\tan\left(f x + e\right)}\right)^{n + 1}}{d {\left(n + 1\right)}} + \frac{2 \, d^{n} \tan\left(f x + e\right)^{-n}}{{\left(n + 3\right)} \tan\left(f x + e\right)^{3}} + \frac{d^{n} \tan\left(f x + e\right)^{-n}}{{\left(n + 5\right)} \tan\left(f x + e\right)^{5}}}{f}"," ",0,"-((d/tan(f*x + e))^(n + 1)/(d*(n + 1)) + 2*d^n*tan(f*x + e)^(-n)/((n + 3)*tan(f*x + e)^3) + d^n*tan(f*x + e)^(-n)/((n + 5)*tan(f*x + e)^5))/f","A",0
44,1,56,0,0.374048," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^4,x, algorithm=""maxima"")","-\frac{\frac{\left(\frac{d}{\tan\left(f x + e\right)}\right)^{n + 1}}{d {\left(n + 1\right)}} + \frac{d^{n} \tan\left(f x + e\right)^{-n}}{{\left(n + 3\right)} \tan\left(f x + e\right)^{3}}}{f}"," ",0,"-((d/tan(f*x + e))^(n + 1)/(d*(n + 1)) + d^n*tan(f*x + e)^(-n)/((n + 3)*tan(f*x + e)^3))/f","A",0
45,1,25,0,0.321023," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^2,x, algorithm=""maxima"")","-\frac{\left(d \cot\left(f x + e\right)\right)^{n + 1}}{d f {\left(n + 1\right)}}"," ",0,"-(d*cot(f*x + e))^(n + 1)/(d*f*(n + 1))","A",0
46,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^2,x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*sin(f*x + e)^2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^4,x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*sin(f*x + e)^4, x)","F",0
48,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^3,x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*csc(f*x + e)^3, x)","F",0
49,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*csc(f*x+e),x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*csc(f*x + e), x)","F",0
50,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*sin(f*x+e),x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*sin(f*x + e), x)","F",0
51,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^3,x, algorithm=""maxima"")","\int \left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*sin(f*x + e)^3, x)","F",0
52,0,0,0,0.000000," ","integrate((b*cot(f*x+e))^n*(a*csc(f*x+e))^m,x, algorithm=""maxima"")","\int \left(b \cot\left(f x + e\right)\right)^{n} \left(a \csc\left(f x + e\right)\right)^{m}\,{d x}"," ",0,"integrate((b*cot(f*x + e))^n*(a*csc(f*x + e))^m, x)","F",0
